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fr                                   PREFACE
grades the path of the student by leading him from the easier to the more difficult dynamical ideas, but it also gives him time to acquire proficiency in the use of his mathematical tools.
As a result of the severe criticisms of Newton's laws of motion by such men as Heinrich Hertz, Ernst Mach, and Karl Pearson, authors of recent text-books on Mechanics have shown a tendency to give either a new set of lawn or none at all. There is no doubt that a subject like Mechanics should start, as in the case of Thermodynamics, with a few simple laws and the entire structure of the science should bo based upon them. In the present work the following law is made the basis of the entire subject;
To every action there is an equal and opposite reaction, or, -.the sum of all the actions to which a body or a part of a body is subject at any instant vanishes.
Four concepts are associated with the term action, namelyt the concepts of /orce, torque, linear kinetic reaction ^ and angular kinetic reaction. These are introduced one at. a time and in connection with the application of the law to .'a certain class of problems. Force is introduced with the equilibrium of a particle (pp. 15,16), torque with the equilibrium of a rigid body (pp. 35, 39, 40), linear kinetic reaction with the motion of a particle (pp. 100-106), angular kinetic reaction with the motion of a rigid body (pp. 21K-221), Thus by introducing the concepts of linear and annular reactions and by extending the meaning of the term action to include these reactions, the fundamental principle of Mechanics is put in the form of a single law, which is equivalent to Newton's laws of motion and which has the advantages of the point of view involved in D'Alembert/H principle. This law has the directness and simplicity of NowtouV
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